scipy.stats.exponpow() | Python

scipy.stats.exponpow() is a method provided by the SciPy library for calculating the probability density function, cumulative distribution function, and quantile function for the Exponential Power Distribution.

The Exponential Power Distribution is a continuous probability distribution that can be used to describe a wide range of real-world phenomena, including the duration of traffic jams, the length of phone calls, and the time between earthquakes.

The exponpow() method takes two arguments - b and loc.

• b (float) is a shape parameter that determines the shape of the distribution.
• loc (float) is a location parameter that shifts the distribution along the x-axis.

The probability density function (PDF) of the Exponential Power Distribution is given by:

$ f(x,b,loc) = b/2 * e^{(-|x-loc|^b)} $

The cumulative distribution function (CDF) of the Exponential Power Distribution is given by:

$ F(x,b,loc) = \int_{-\infty}^{x} f(x,b,loc) dx = 1 - e^{(-|x-loc|^b)} $

Syntax

scipy.stats.exponpow(b, loc=0)

• b: Float or array_like of floats. Shape parameter(s).
• loc: Float or array_like of floats. Location parameter(s).

Example

This example shows how to use scipy.stats.exponpow() method to generate a probability density histogram.

import scipy.stats as stats
import numpy as np
import matplotlib.pyplot as plt

b = 2 # shape parameter
loc = 0 # location parameter

# Generate some random data
data = stats.exponpow.rvs(b, loc, size=100000)

# Create histogram
plt.hist(data, bins=100, density=True, alpha=0.7, color='purple')

# Calculate PDF and plot
x = np.linspace(stats.exponpow.ppf(0.01, b, loc), stats.exponpow.ppf(0.99, b, loc), 1000)
plt.plot(x, stats.exponpow.pdf(x, b, loc), 'r-', lw=2)

plt.show()

In the code above, we first set the shape parameter b to 2 and the location parameter loc to 0. We then generated some random data using the rvs() method and plotted a histogram of the data using the hist() method. Finally, we calculated and plotted the probability density function using the pdf() method.

Conclusion

In conclusion, scipy.stats.exponpow() method is a useful tool for working with the Exponential Power Distribution in Python. With the ability to generate random data, calculate PDF and CDF, and plot histograms and graphs, this method provides a comprehensive set of tools for working with this distribution.